Wolves 3 Southampton 0
But Wolves did grab a third with just 19 minutes gone. Saganowski, who bagged a hat-trick at Molineux in Saints' 6-0 success in 2007, brought down David Edwards and Jones found the roof of the net with the resulting penalty.
Saints boss Mark Wotte introduced Jason Euell and Bradley Wright-Phillips at the interval in an attempt to salvage something from the game.
And Euell almost pulled one back in the 51st minute but he failed to get any real contact on the ball as it found its way back to him following Wayne Hennessey's smart stop from Saganowski.
From then on it was Wolves who came closest to adding to their tally with Vokes, Keogh and substitute Marlon Harewood - making his home debut - all going close.
Wright-Phillips came within inches of netting a consolation for the visitors but his shot after a jinking run was deflected just wide by the impressive Craddock.
And as the clock ran down it was Wolves who were comfortably left celebrating their first home victory over Saints since 1979.
A Mexican wave went around Molineux in the closing stages, with the focus now turning to what Wolves' promotion rivals can muster in reply.
